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What you will learn in Build a Robo-Advisor with Python (From Scratch)

Automate your financial and investment decisions

by Rob Reider and Alexander Michalka

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Chapter by chapter

Concepts explained in this book

• meanAn arithmetic average return is the sum of periodic investment returns divided by the number of periods.
• wash-sale ruleThe wash-sale rule is a tax rule that generally disallows recognizing an investment loss when the taxpayer acquires a substantially identical security within the specified surrounding period.
• tax lotA tax lot is a distinct group of investment shares acquired in a particular transaction and tracked with its acquisition details for tax purposes.
• risk contributionA risk contribution is the fraction of a portfolio's variance risk attributable to an asset or subportfolio, calculated as its covariance with the full portfolio divided by the portfolio variance.
• reward signalA reward is a numerical feedback signal representing the benefit or cost an agent receives after taking an action.
• Black–Litterman modelThe Black–Litterman model is an asset-allocation framework that combines market-implied equilibrium returns with investor views to produce adjusted return estimates and portfolio weights.
• realized gain or lossA gain on an investment that becomes recognized for tax or accounting purposes when the investment is disposed of.
• covariance matrixA covariance matrix is a square symmetric matrix containing asset variances on its diagonal and pairwise covariances off the diagonal.
• asset allocationAsset allocation is the distribution of an investment portfolio across asset classes selected to match an investor's risk tolerance and objectives.
• risk parityWeighted risk parity is a portfolio-construction technique that assigns different optimization weights to instruments so aggregate risk contributions follow a specified asset-class structure.
• portfolio optimizationPortfolio optimization is the technique of selecting portfolio holdings or weights by optimizing a specified investment objective.
• normal distributionA normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped density determined by its mean and standard deviation.
• constraintA constraint is a mathematical restriction that limits the values or combinations permitted for optimization variables.
• robo-advisorThe provision of automated investment advice or portfolio-management services through algorithmic software.
• opportunity costThe value of a benefit forgone when choosing one action prevents or limits an alternative action.
• risk-free assetAn investment whose return over a specified horizon is known with certainty and is not exposed to interim price or reinvestment uncertainty.
• asset locationAsset location is the strategic placement of assets among account types to improve after-tax investment outcomes.
• dynamic programmingDynamic programming is a computational technique that solves sequential decision problems by decomposing them into states, actions, transition probabilities, and recursively computed value functions.
• portfolio weightA portfolio weight is the proportion of a portfolio allocated to a particular asset, with weights commonly constrained to sum to one.
• tax bracketA tax bracket is a range of taxable income to which a specified marginal tax rate applies.
• standard deviationStandard deviation is a measure of the dispersion of investment returns around their mean, commonly interpreted as return volatility.
• policyA policy is a rule or mapping that specifies which action an agent should take for each state.
• hierarchical risk parityHierarchical risk parity is a portfolio-construction technique that clusters assets by correlation, orders the covariance matrix by those clusters, and allocates weights through recursive bisection.
• investor viewAn investor view is a stated expectation about the relative or absolute future performance of one or more assets or portfolios.
• reinforcement learningReinforcement learning is a machine-learning approach in which an agent learns a decision policy through interactions with an environment and feedback from rewards or penalties.
• transition probabilityA transition probability is the probability of moving from one state to a particular subsequent state under an action or allocation.
• cost-basis adjustmentA cost-basis adjustment is a change to an investment's tax basis to account for a tax-relevant transaction such as a wash sale.
• agglomerative clusteringAgglomerative clustering is a bottom-up clustering technique in which each object starts as a singleton cluster and clusters are successively combined.
• distance matrixA distance matrix is a square array whose entries represent pairwise dissimilarities between objects.
• hierarchical clusteringHierarchical clustering is a clustering technique that organizes objects into progressively combined or subdivided groups according to a distance measure.
• linkage matrixA linkage matrix is a tabular numerical representation of the successive cluster combinations, their intercluster distances, and the sizes of the resulting clusters.
• quasi-diagonalizationQuasi-diagonalization is the reordering of a matrix so that similar or closely related items are positioned near one another, producing an approximately block-diagonal structure.
• recursive bisectionRecursive bisection is a portfolio-weighting technique that repeatedly splits ordered asset groups into two parts and adjusts their weights according to the variances of their subportfolios.
• correlationCorrelation is a statistical measure of the direction and strength of dependence between two variables or asset returns.
• tax dragTax drag is the reduction in investment growth or portfolio value caused by taxes on income, gains, or distributions.
• tax deferralTax deferral is the postponement of tax recognition or payment until a later taxable event.
• tax-loss harvestingThe optimization of investment transactions to capture tax losses or otherwise improve after-tax returns.
• alphaAlpha is the intercept of a return regression and represents performance not explained by the benchmark or specified risk factors.
• convex optimizationOptimization with a convex objective function and a convex feasible set, for which efficient algorithms can provide globally optimal solutions.
• longevity riskLongevity risk is the risk of living longer than expected and exhausting financial resources during one's lifetime.
• after-tax valueAfter-tax value is the value of an investment or account balance remaining after applicable taxes are deducted.
• posterior probabilityA posterior distribution is a probability distribution representing updated beliefs about an unknown quantity after incorporating data or observations.
• bid-ask spreadA bid-ask spread is the difference between the highest price a buyer offers and the lowest price a seller accepts for a traded investment.
• PythonA general-purpose, high-level programming language with dynamic typing and extensive support for scripting, data analysis, and application development.
• optimal sequencing of withdrawalsA planned method for determining how and when assets are withdrawn from investment accounts.
• Monte Carlo simulationA Monte Carlo simulation is a computational technique that estimates outcomes by repeatedly sampling from specified probability distributions or scenarios.
• feasible regionA feasible set is the set of variable values that satisfy all constraints of an optimization problem.
• prior probabilityA prior distribution is a probability distribution representing beliefs about an unknown quantity before incorporating observed data.
• actionAn action is a decision selected by an agent that can change the state of its environment.
• stateA state is a representation of the relevant current variables of an environment that determine an agent's possible decisions.
• cost basisCost basis is the tax-accounting value assigned to an investment for determining taxable gain or loss when it is disposed of.
• glide pathA glide path is a sequence of portfolios or asset allocations that gradually changes an investor's risk level over time.
• required minimum distributionA required minimum distribution is the minimum amount that must be withdrawn annually from certain tax-advantaged retirement accounts after the account owner reaches a legally specified age.
• tracking errorTracking error is the variability or magnitude of an investment's return difference from the benchmark or reference portfolio it is intended to follow.
• betaBeta is a measure of an asset's sensitivity to movements in the overall market, with the market portfolio conventionally assigned a beta of one.
• time horizonAn investment horizon, or time horizon, is the period over which an investment is expected to be held or evaluated.
• tax savingsA reduction in tax liability attributable to a deduction, exclusion, credit, or other tax-favored treatment.
• binomial treeA discrete lattice model that represents possible successive movements in an asset price for valuing derivatives.
• option-priceA Python package that computes option prices using supported analytical and numerical pricing methods.
• option pricingOption pricing is the process of estimating the fair value of a financial option from its contractual terms and the behavior of relevant underlying variables.
• option valueThe monetary value of an option contract, reflecting the potential benefit from exercising its rights.
• put optionA financial contract giving its holder the right, but not the obligation, to sell an underlying asset at a specified strike price before or at expiration.
• exchange-traded fundAn exchange-traded fund is an investment fund whose shares trade on a stock exchange and typically track an index, asset class, or portfolio strategy.
• backtestingBacktesting is the evaluation of an investment strategy by simulating its application to historical market data.
• cvxpyCVXPY is a Python library for modeling and solving convex optimization problems with a declarative mathematical syntax.
• closed tax lotA closed tax lot is a tax lot whose remaining share quantity has reached zero after disposal.
• tax efficiencyTax efficiency is the degree to which an investment strategy minimizes taxes relative to its returns or transactions.
• threshold-based rebalancingThreshold-based rebalancing is a rebalancing method that trades when an asset's portfolio weight deviates beyond a specified tolerance from its target.
• turnoverPortfolio turnover, or turnover rate, is the proportion of a portfolio or fund's holdings sold or replaced during a specified period.
• cyclically adjusted price-to-earnings ratioA stock valuation ratio that divides price by inflation-adjusted average earnings over the prior ten years.
• excess returnAn investment return measured above the return of a specified risk-free benchmark.
• price-to-earnings ratioA valuation ratio comparing a stock's market price with its earnings per share.
• total returnA total return index measures investment performance including both price changes and reinvested cash distributions.
• yieldThe income rate or implied return generated by a debt security, commonly expressed as a percentage of its value or face amount.
• infinity normThe infinity norm of a vector is the maximum of the absolute values of its components.
• inner productThe dot product is an operation that sums the pairwise products of corresponding components of two vectors to produce a scalar.
• capital asset pricing modelThe capital asset pricing model is a financial model that estimates an asset's expected return from the risk-free rate, market expected return, and the asset's sensitivity to market returns.
• wealth pathA wealth path is a chronological sequence of portfolio wealth values representing one simulated financial trajectory.
• constraint classA constraint class is a software class representing an optimization constraint and generating its solver-specific form.
• full-investment constraintA full-investment constraint requires the total amount invested to equal a specified amount.
• long-only constraintA long-only constraint requires every portfolio weight to be nonnegative, prohibiting short positions.
• inflation riskThe risk that rising prices will reduce the purchasing power of money or the real value of investment returns.
• substantially identical instrumentA substantially identical security is an investment security considered equivalent to another security for applicable tax-law purposes.
• portfolio rebalancingA rule or procedure for deciding when and how portfolio holdings should be traded toward target allocations.
• reference portfolioA reference portfolio is a portfolio selected as the baseline against which another portfolio's characteristics or performance are compared.
• equilibrium returnAn equilibrium return is an expected investment return implied by market portfolio weights, investor expectations, and risk aversion.
• ETF creation and redemptionETF creation and redemption is the mechanism by which authorized participants exchange ETF shares for baskets of underlying securities and vice versa.
• tax rateA tax rate is the percentage or marginal proportion applied to a specified taxable base to determine tax owed.
• taxable accountA taxable account is an investment account whose income, gains, or distributions are generally subject to taxation rather than receiving retirement-account tax treatment.
• Roth IRAA Roth IRA is an individual retirement account whose qualified withdrawals are generally tax-free and whose contributions are not generally tax-deductible.
• inflationInflation is a sustained increase in the general price level of goods and services that reduces the purchasing power of money.
• information ratioThe information ratio is the expected return above a benchmark divided by the volatility of the portfolio's return difference from that benchmark.
• market returnMarket return is the return of the broad market portfolio over a specified period.
• consumptionConsumption is the use of resources for present satisfaction, including expenditures from wealth.
• spendingSpending is the use of financial resources to purchase goods, services, or other benefits.
• conditional probabilityConditional probability is the probability of an event given that another event or condition is known to occur.
• likelihoodA likelihood is the probability of observed data conditional on a specified parameter value or hypothesis.
• SciPySciPy is a Python library of algorithms and functions for scientific and numerical computing, including optimization, integration, root-finding, and statistics.
• curse of dimensionalityThe curse of dimensionality is the rapid growth in computational and data requirements as the number of states, variables, or dimensions in a problem increases.
• ordinary incomeOrdinary income is taxable income arising from sources such as wages, interest, and non-preferentially taxed distributions rather than preferentially taxed capital gains.
• capital gains tax rateA capital gains tax rate is the tax rate applied to taxable gains from disposing of an investment.
• covarianceCovariance is a measure of how two asset returns vary together, combining their volatilities with their correlation.
• volatilityVolatility is a statistical measure of the variability of an asset's or portfolio's returns.
• esg ratingA quantitative assessment of an investment's environmental, social, and governance characteristics.
• stepped-up cost basisA stepped-up cost basis is a tax basis adjustment that resets an inherited asset's basis to its fair market value at the owner's death or another legally specified date.
• management feeAn expense ratio is the percentage of an investment fund's assets charged annually to cover its operating expenses.
• Sharpe ratioThe Sharpe ratio is the expected return above the risk-free rate divided by the investment's volatility, measuring expected reward per unit of risk.
• convexityA mathematical property of functions or sets that ensures line-segment combinations remain compatible with global optimization guarantees.
• high-growth stock fundA high-growth stock fund is an investment fund focused on stocks associated with expectations of comparatively high future growth.
• risk-aversion parameterA risk-aversion parameter is a coefficient in an investment objective that controls the penalty assigned to portfolio risk relative to expected return.
• time value of moneyThe time value of money is the principle that a given amount of money available today has greater economic value than the same nominal amount available in the future because it can earn a return.
• backward inductionBackward induction is a solution method that computes decisions or values from a final state backward through earlier states.
• cumulative distribution functionA cumulative distribution function gives the probability that a random variable is less than or equal to a specified value.
• efficient frontierThe efficient frontier is the set of portfolios offering the highest expected return for each level of risk or the lowest risk for each expected return.
• socially responsible investingSRI, or socially responsible investing, is an investment approach that selects investments according to their perceived social or environmental benefits.
• minimum-variance frontierThe minimum-variance frontier is the set of portfolios that achieve the lowest possible variance for specified expected returns when no risk-free asset is included.
• dollar-weighted returnA dollar-weighted return is an investment return that accounts for the timing and amount of external cash flows, commonly through an internal-rate-of-return calculation.
• matrix-matrix multiplicationMatrix multiplication is an algebraic operation that combines rows of one matrix with columns of another to produce a new matrix or vector.
• risk-adjusted returnRisk-adjusted return, or risk-adjusted performance, is investment performance evaluated in relation to the amount or type of risk taken to achieve it.
• discount rateA discount rate in reinforcement learning is a parameter that determines how strongly future rewards are weighted relative to immediate rewards.
• epsilon-greedyEpsilon-greedy is an action-selection strategy that chooses a random action with probability epsilon and a currently best-known action otherwise.
• exploration-exploitation trade-offThe exploration-exploitation tradeoff is the decision problem of balancing actions that gather new information against actions expected to yield the best known outcome.
• Q-learningQ-learning is a model-free reinforcement-learning algorithm that estimates the value of taking each action in each state and uses those estimates to derive a policy.
• action-value functionA Q-function maps a state and an action to the estimated cumulative reward obtained by taking that action and following a policy afterward.
• temporal-difference errorA temporal difference is the discrepancy between a current value estimate and a reward-adjusted estimate based on a subsequent state.
• Roth conversionA Roth conversion is a transaction that transfers or converts assets from a traditional retirement account into a Roth IRA, generally creating taxable income at conversion.
• discount rateA financial discount rate is an expected rate of return used to convert a future cash flow into its value today.
• annuityAn annuity is a financial contract that provides a series of payments, often for the holder's lifetime.
• authorized participantA designated financial-market participant permitted to exchange an exchange-traded fund's underlying asset basket for fund shares and vice versa.
• certainty equivalent valueA certainty equivalent is the guaranteed amount that provides the same utility as a specified risky prospect.
• risk toleranceRisk tolerance is an investor's willingness to accept uncertainty and potential investment losses in exchange for possible returns.
• risk-free returnThe risk-free rate is the return associated with an investment assumed to have no default risk over the relevant time horizon.
• ordinary income tax rateAn ordinary income tax rate is the tax rate applied to income taxed under ordinary income-tax rules rather than preferential capital-gains rules.
• autoregressive modelA time-series model in which the current value depends linearly on one or more previous values and a random error term.
• mutual fundAn investment fund whose shares are bought from or sold to the fund provider at a price based on the value of the fund's holdings, typically once per trading day.
• present valuePresent value is the value today of future cash flows discounted to reflect the timing of those cash flows.
• evaluate_all_harvestevaluate_all_harvest is a book-specific function that evaluates harvesting trades across all holdings in an exchangeable ETF set.
• evaluate_harvestevaluate_harvest is a book-specific function that evaluates whether harvesting a single tax lot with a specified replacement investment has positive net benefits.
• net asset valueThe per-share value of an investment fund's net underlying assets, calculated as total assets minus liabilities divided by shares outstanding.
• periodic rebalancingA rebalancing strategy that generates trades when the current date appears in a specified list of rebalancing dates.
• inherited IRAAn individual retirement account received by a beneficiary after the original account owner's death and governed by beneficiary-specific distribution rules.
• traditional IRAA traditional IRA is an individual retirement account whose contributions or earnings receive tax treatment that generally defers taxation until withdrawal.
• dynamic modelA lifecycle model is an economic model of decisions and resources across multiple periods of an individual's or household's life.
• marginal tax rateA marginal tax rate is the tax rate applied to the next unit of taxable income within a tax system.
• time-weighted returnA time-weighted return is an investment return calculated by linking subperiod returns between external cash flows so that the timing and size of investor contributions do not determine the result.
• mortality tableA mortality table is a statistical table giving the probability of death or survival for members of a population at different ages.
• do-not-increase-deviation constraintA do-not-increase-deviation constraint prevents an optimized position from being farther from its target than the current position.
• do-not-trade-past-target constraintA do-not-trade-past-target constraint prevents trading an asset from one side of its target position to the other side.
• generate_constraintgenerate_constraint is a method that constructs the optimization constraint represented by a constraint object from supplied problem data.
• generate_objectivegenerate_objective is a method that constructs an optimization objective from supplied portfolio and problem data.
• max-deviation constraintA max-deviation constraint bounds each optimized position within an interval around its target position.
• MinTaxObjectiveMinTaxObjective is a book-specific optimization objective that selects trades to minimize their total tax cost.
• MinTrackingErrorObjectiveMinTrackingErrorObjective is an optimization objective that selects portfolio trades to minimize tracking error relative to a target portfolio without considering taxes.
• objective classAn objective class is a software class that generates an objective function for portfolio optimization.
• volatility-based deviation constraintA volatility-based deviation constraint bounds position deviations according to asset volatility, allowing larger deviations for lower-volatility assets.
• budget constraintA budget constraint is an equation or inequality limiting feasible spending and investment choices according to available resources.
• consumption smoothingConsumption smoothing is the practice of distributing consumption more evenly across time rather than concentrating it in particular periods.
• fsolvefsolve is a SciPy function that numerically solves nonlinear equations by finding their roots.
• VariableVariable is the CVXPY constructor for creating symbolic decision variables with a specified shape.
• retirement accountAn investment account that receives preferential tax treatment for contributions, investment growth, withdrawals, or some combination of these.
• taxA compulsory charge imposed by a government on income, transactions, property, or other taxable bases.
• payout rateA payout rate is the annual percentage of an asset's value distributed as dividends or interest.
• environmentAn environment is the external system in which a reinforcement-learning agent takes actions and from which it receives observations and rewards.
• Markov propertyThe Markov property is the condition that the probabilities of future states depend on the current state and action but not on earlier history.
• transaction costA transaction cost is an expense incurred when buying, selling, transferring, or modifying an asset or contract.
• ETF premium or discountThe amount by which an ETF's market price is above or below its net asset value.
• GARCH modelA generalized autoregressive conditional heteroskedasticity model estimates time-varying conditional volatility from past observations and volatility shocks.
• defined-benefit pension planA pension plan that promises retirement payments determined by a formula, rather than by an individual's account balance.
• adjusted close priceAn adjusted closing price, or adjusted close, is a historical closing price adjusted for corporate actions such as dividends and stock splits.
• volatility clusteringVolatility clustering is the tendency for large changes in returns to be followed by large changes and small changes to be followed by small changes.
• CPI-UCPI-U is the Consumer Price Index for All Urban Consumers, a measure of average consumer prices paid by urban households in the United States.
• inflation rateThe inflation rate is the percentage rate at which the general price level of goods and services increases over a specified period.
• mean-reverting processA mean-reverting process is a stochastic process whose values tend to move back toward a long-run average.
• Ornstein–Uhlenbeck processAn Ornstein–Uhlenbeck process is a continuous-time stochastic process that is pulled toward a long-run mean while being perturbed by random noise.
• financial advisorA financial advisor is a professional who advises clients on financial goals, plans, and investments and may manage their money.
• smart betaSmart beta is an investment approach that selects or weights securities using systematic rules based on factors or characteristics beyond traditional market capitalization.
• financial leverageLeverage is the use of borrowed funds to increase the size of an investment position relative to the investor's own capital.
• 95% worst-case lossA 95% worst-case loss is a loss threshold intended to be exceeded in only the worst five percent of modeled outcomes over a specified horizon.
• loss aversionLoss aversion is a behavioral bias in which losses have greater psychological impact than comparable gains.
• effective tax rateAn effective tax rate is the percentage of a sale's gain or loss used to determine the applicable tax impact for a particular holding.
• incomplete tradingIncomplete trading is a rebalancing approach that restores an asset only partway toward its target weight rather than fully returning it to target.
• tax heuristicA tax heuristic is a rule of thumb for selecting investment transactions or holdings to improve their tax consequences.
• dividendA dividend is a distribution of a company's earnings or capital to its shareholders.
• individual position constraintAn individual position constraint limits the allocation or magnitude of a single portfolio holding.
• interestInterest income is compensation received for lending money or holding an interest-bearing investment.
• qualified dividendA qualified dividend is a dividend that meets applicable tax-law requirements for taxation at preferential capital-gains rates.
• relative weight constraintA relative weight constraint limits how far the weights of two or more assets may differ in ratio or absolute amount.
• rate conversionRate conversion is a tax strategy that offsets higher-taxed short-term gains with losses and later realizes replacement-asset gains under lower long-term capital-gains rates.
• historical dataHistorical data is recorded information about past asset prices, dividends, and other market events.
• asset classA category of investments that share broadly similar financial characteristics and market behavior.
• historical returnA historical return is the realized percentage change in an investment's value over a completed past period.
• state taxA state tax is a tax imposed by a subnational state government on specified income, transactions, property, or other taxable bases.
• arch_modelarch_model is a Python API function in the arch library that constructs ARCH-family volatility models.
• temporal autocorrelationAutocorrelation is the correlation between a time series and a lagged version of itself.
• volatility mean reversionVolatility mean reversion is the tendency of volatility to move back toward a long-run or pre-shock level after a temporary deviation.

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